It really depends on the child. I use a form of time out with my daughter when she is angry. She cannot stop herself from screaming (literal screams), saying rude things and generally behaving inappropriately. I send her to her room to cool off and give me a few minutes to regroup. She comes out when she's ready and is able to behave in a civilized manner.
When she was little and upset, I could not be in the same room as her or it would set her off all over again. It really was like hitting the reset button her forty five minute melt downs. She is on the spectrum, so that probably has something to do with it.
For me to hug her or try to soothe her is counter productive to say the least. But that time alone is enough for her to calm down and get a fresh perspective.
My son on the other hand needs to be held and comforted when he is upset. I would no more leave him to deal with his big overwhelming feelings than I would leave him unsupervised with markers. He gets really upset and screams until I pick him up and talk to him. Once he hears that his anger is heard and understood, he can move on with his day. But he needs to know that he is heard and someone cares.
That being said, I am not going use time out to punish them. It's pretty illogical if you think about it. Kids aren't thinking about whatever they did to end up in time out. Or at least not in the way they're supposed to be thinking. They are thinking of the injustice of it all and how unfair this situation is. I don't blame them one bit for that, either. Talking when they are calm works a lot better.
I can understand why people use time out. They don't know what else to do. They know they shouldn't hit or yell, so now what? They whole parenting without punishing is a pretty out there idea for most people. I know it had to be right up there with the earth is flat when I first heard it. I felt so sorry for those kids because I believed that their parents were too busy trying to be smarter than everyone else in the room to really parent their children and those poor children were going to pay a very steep price as they got older. But once I learned what to do instead of what not to do, it clicked. It's not letting them do whatever they want, it's setting limits that really do mimic the real world.